Branched polymers offer highly tunable properties and functionality. However, obtaining soluble, sufficiently branched macromolecules within the desired molecular weight range by conventional radical polymerization (RP) is still a challenging task, as there is no systematic investigation of this problem. In this work, we develop a three-dimensional coarse-grained molecular-dynamics model of RP in the presence of a divinyl crosslinker (CL) and a chain-transfer agent (CTA). Simulations are based on the Kremer-Grest bead-spring framework with Langevin dynamics under good-solvent conditions and include stochastic reactions: initiation, propagation, crosslinking, chain transfer, and termination. Macromolecular architecture is quantified by graph-based decomposition into dangling ends, elastically active subchains, and cycles, and by extracting an effective fractal dimension from the scaling of the radius of gyration with molecular mass. Two distinct regimes emerge. At low CTA content, gelation occurs at relatively small conversion; a rapidly growing network quickly dominates the molecular-weight distribution, which broadens substantially, while the population of isolated branched macromolecules diminishes. Increasing the CTA content shifts gelation toward high conversion, enabling the formation of a stable sol fraction enriched in high-molecular-weight branched molecules. Phase diagrams over 2%-16% crosslinker and 0%-8% CTA identify a simple optimal condition: the gel-point conversion approaches unity along [CL] = 2[CTA], consistent with an average of two effective intermolecular attachment points per growing chain. Along this optimum line, higher crosslinker content produces more compact branched macromolecules, implying higher coil-overlap concentrations and lower intrinsic viscosities at fixed molecular weight. These results provide practical, quantitative guidance for selecting reagent ratios to synthesize soluble branched polymers via standard RP.

HYPOTHESIS:Micelles formed by copolymers with mixed solvophobic blocks have attracted much attention lately. It is expected that changing the mixed blocks sequence can be used as a tool to influence the micellization behavior in a way that is not equivalent to simply varying the incompatibility parameter for pure diblock-copolymers. Simulations: By using coarse-grained simulations, the micellization behavior of copolymers with twelve types of solvophobic blocks, which differed in the fraction f as well as the sequence of solvophilic units in the solvophobic blocks, was studied. To enable quantitative comparison of systems with different f, an "effective" incompatibility parameter was introduced. FINDINGS:The micelles size distributions and dynamics were found to be significantly dependent on both f and the fine details of the sequence. When the solvophobic block sequences were obtained statistically using a model of copolymerization, a strong influence of the reactivity ratios on the resulting micelles was found. Even a moderate tendency to form gradient-like sequences resulted in a noticeable increase in the micelles size. The dynamic properties of the micelles were studied by investigating the rate at which the chains escape from them. The addition of soluble units into the solvophobic block was shown to dramatically decrease the tendency to form kinetically frozen states; gradient-like sequences demonstrated more sluggish dynamics. The physical reasons for the observed peculiarities are discussed in detail.

Redox-active polymer gels are promising materials for various applications, such as energy conversion and storage systems, organic electronics, soft-robotics, sensors and others. This is in part due to the remarkable structural tunability of these materials. The gel may adopt different conformations depending on the crosslinking density, solvent temperature and other conditions. These parameters affect its behavior, including the dynamics of the charge transport between the redox groups grafted to the polymer subchains, which is of utmost importance for electrochemical applications. Here, we employed coarse-grained molecular dynamics simulation to investigate the impact of crosslinking, redox group content and solvent quality on both subchain mobility and charge transport speed. In particular, unexpected behavior of the system under the theta-solvent condition was found and analyzed. The obtained results provide useful guidelines to facilitate the best conditions for enhanced "redox induced" conductivity in polymer gels, which would help the development of redox-flow batteries and other electrochemical devices.

Using molecular dynamics simulations, we explore the impact of correlated monomer activity and star topology on the structure and dynamics of active polymers. Unlike uncorrelated active Brownian particle (ABP) stars, correlated activity induces a rather steep stretching of the star polymer at intermediate activity levels. This stretching is characterized by transitions between distinct, metastable states defined by the coordinated movement of the arms, leading to novel collective dynamics. The behavior is consistent with experimental observations of active oligomers, highlighting the critical role of activity correlations for the understanding and modeling of active polymers.

In this work, we study the effect of covalent bonding on the behavior of non-equilibrium systems with the active force acting on particles along their velocity. Self-ordering of single particles does not occur in this model. However, starting from some critical polymerization degree, the ordered state is observed. It is homogeneous and exhibits no phase separation. In the ordered state, the chains prefer a near-two-dimensional configuration and all move in one direction. Importantly, the self-ordering is obtained only at intermediate active force magnitudes. At high magnitudes, the transition from the disordered to ordered state is suppressed by the swelling of the chains during the transition, as we show by the transition kinetics analysis. We demonstrate the bistable behavior of the system in a particular range of polymerization degrees, amplitudes of active force, densities, and thermostat temperatures. Overall, we show that covalent bonding greatly aids the self-ordering in this active particle model, in contrast to active Brownian particles.

In this paper, we provide a thorough electrochemical study of redox-active nanosized cationic gels which are promising materials for redox flow battery electrolytes. We use two-step synthesis under mild aqueous conditions: precipitation polymerization of nanogels based on poly-(N-isporopylacrylamide-co-N-(3-aminopropyl) methacrylamide hydrochloride) (PNIPAM-co-APMA), and grafting of redox-active 4-(3-carboxypropanamido)TEMPO units to the nanogels. We demonstrate stable reduction-oxidation behavior of such nanogels and suggest a universal approach to evaluate the "effective" concentration and diffusion coefficient of redox-active groups grafted to nanogel particles. For the TEMPO-grafted PNIPAM-co-APMA nanogels we find the "effective" concentration of TEMPO-groups to be approximately 50 % of their total concentration and demonstrate an increase of the "effective" concentration upon electrode rotation. Also, we investigate electron transfer kinetics of redoxactive nanogels and provide an evidence that the adsorbed layer of nanogels facilitates electron transfer.

Polymer microgel particles decorated with redox-active functional groups are a new and promising object for electrochemical applications. However, the process of charge exchange between an electrode and a microgel particle carrying numerous redox-active centers differs fundamentally from charge exchange involving only molecular species. A single act of contact between the microgel and the electrode surface may not be enough to fully discharge the microgel, and partial charge states are to be expected. Understanding the specifics of this process is crucial for the correct analysis of the data obtained from electrochemical experiments with redox-active microgel solutions. In this study, we employed coarse-grained molecular dynamics to investigate in detail the act of charge transfer from a microgel particle to a flat electrode. The simulations take into account both the mobility of functional groups carrying the charge, which depend on the microgel architecture and the charge exchange between the groups, which can accelerate the propagation of charge within the microgel volume. A set of different microgel systems were simulated in order to reveal the impact of their characteristics: fraction of redox-active groups, microgel molecular mass, cross-linker content, cross-linking topology, and solvent quality. We have found trends in microgel composition leading to the most efficient charge transfer kinetics. The obtained results would be useful for understanding experimental results and for optimizing the design of redox-active microgel particles aimed at faster discharge rates.

Polymer microgels, micrometer-sized cross-linked polymer particles, are considered to be a promising type of advanced materials for a wide range of applications. To enhance the microgels' applicability, it is essential to incorporate various functional groups into a microparticle polymer network. Yet, the availability of functional groups for the interaction with surroundings depends strongly on the properties of the polymer network and has a great impact on further effective usage. In this theoretical study, we address this question and, with the help of coarse-grained molecular dynamics computer simulations, assess the segmental mobility and accessibility of functional groups bound to polymer network depending on microgel architecture and solvent quality. Additionally, we evaluate the minimum number of functional groups needed to facilitate the hopping mechanism between the functional groups (i.e., charge transfer). As an example of practical implementation of the obtained results, we estimate the optimal network topology for redox-active microgels to provide the maximum charge capacity for the dispersion electrolyte in redox-flow batteries.

For the first time, double stimuli-responsive properties of poly(N-isopropylacrylamide) (PNIPA) and poly(1-vinylimidazole) (PVIM) block copolymers in aqueous solutions were studied. The synthesis of PNIPA60-b-PVIM90 and PNIPA28-b-PVIM62-b-PNIPA29 was performed using reversible addition–fragmentation chain transfer (RAFT) polymerization. The polymers were characterized by size exclusion chromatography and 1H NMR spectroscopy. The conformational behavior of the polymers was studied using dynamic light scattering (DLS) and fluorescence spectroscopy (FS). It was found that PNIPA and block copolymers conformation and ability for self-assembly in aqueous medium below and above cloud point temperature depend on the locus of hydrophobic groups derived from the RAFT agent within the chain. Additionally, the length of PVIM block, its locus in the chain and charge perform an important role in the stabilization of macromolecular micelles and aggregates below and above cloud point temperature. At 25 °C the average hydrodynamic radius (Rh) of the block copolymer particles at pH 3 is lower than at pH 9 implying the self-assembling of macromolecules in the latter case. Cloud points of PNIPA60-b-PVIM90 are ~43 °C and ~37 °C at a pH of 3 and 9 and of PNIPA28-b-PVIM62-b-PNIPA29 they are ~35 °C and 31 °C at a pH of 3 and 9. Around cloud point independently of pH, the Rh value for triblock copolymer rises sharply, achieves the maximum value, then falls and reaches the constant value, while for diblock copolymer, it steadily grows after reaching cloud point. The information about polarity of microenvironment around polymer obtained by FS accords with DLS data.

In this work we developed a RAFT polymerization model taking into account the main reactions of the experimental RAFT process and implemented that model in dissipative particle dynamics (DPD). With a help of a kinetic model based on the same reaction routine, we investigated the question of how to simulate realistic reactions using such models. We showed that a simultaneous M-fold increase of the initiation probability p_i and an M-fold decrease of the termination probability p_t does not result in significant changes in the chain length distribution. If the RAFT/initiator ratio is small, a simplified model with no termination and immediate radical formation can be used with good enough accuracy. After that we directly compared the reaction behavior within the kinetic model and DPD. We showed that steric restrictions, which were not present in the kinetic model, can introduce noticeable changes in the system behavior. Finally, we studied the influence of the incompatibility on the RAFT polymerization process on an example classical implementation of polymerization-induced self-assembly (PISA). We showed that in systems with incompatible species number of activation-deactivation cycles does not always reflect the dispersity of the resulting chain ensemble. Moreover, we demonstrated that specifically the incompatibility between the RAFT end group and other species can have a large effect on the polymerization results.

It is well-known that the architecture of macromolecules plays an important role in the hydrodynamics and viscosity of its semi-diluted solutions. However, the systematic study of the rheology of macromolecules with complex topology, such as microgels, remains a difficult task. In this work, we use the computer simulations methods of non-equilibrium molecular dynamics to study the viscous properties of randomly cross-linked microgels and compare it to multiple reference systems (linear chains, 10-arm star polymers and hard spheres). We show that the microgel cross-linking density and, thus, the particle shape, plays crucial role in its shear viscosity. Also, in contrast to a simpler polymer systems, microgel dispersions in good solvent show much less shear thinning.

In this work, we studied the equilibrium structures formed by a single (AB)k multiblock copolymer chain. Within our model, the interactions between the A-type beads were repulsive and the B-type beads could form pairwise reversible bonds with each other (BB-bonds). Our goal was to investigate how the formation of pairwise reversible bonds between the A-type beads and the B-type beads (AB-bonds) affected the structure of the chain. We observed the formation of well-studied intramolecular micelles when the AB-bonds were absent; however, the chain folding changed dramatically when the formation of the AB-bonds was introduced. In this case, the multiblock copolymer formed a globule, which had a unique heterogeneous checkerboard-like distribution of the contact density. We discovered that contacts of beads of different types (i.e., AB-contacts) occurred much more frequently than contacts of beads of the same type (i.e., AA- and BB-contacts) in these structures. This effect can be explained by a simple model of chemical equilibrium in a two-component fluid of reversibly interacting particles, which can be solved exactly. This novel type of folding can serve as a basic model for any (AB)k multiblock copolymer chain with a non-vanishing attraction between A and B blocks.

Polymer fibers consist of macromolecules oriented along the fiber axis. Better alignment of chains leads to an increased strength of the fiber. It is believed that the key factor preventing formation of a perfectly oriented fiber is entanglement of polymers. We performed large-scale computer simulations of uniaxial stretching of semicrystalline ultrahigh molecular weight polyethylene. We discovered that there is an optimal number of entanglements per macromolecule necessary to maximize chain orientation in a fiber. Polymers that were entangled too strongly formed less oriented fibers. On the other hand, when polymers had too few entanglements per chain, they disentangled during stretching, and the strong fiber was not formed. We constructed a microscopic analytical theory describing both the fiber formation and disentanglement processes. Our work presents a novel view on the role of entanglements during fiber production and predicts the existence of a single universal optimal number of entanglements per chain maximizing the fiber quality: approximately $10^2$ entanglements.

Correction for 'Effect of network topology and crosslinker reactivity on microgel structure and ordering at liquid-liquid interface' by Rustam A. Gumerov et al., Soft Matter, 2022, 18, 3738-3747, https://doi.org/10.1039/D2SM00269H.

Polymer microgels synthesized in silico were studied at a liquid-liquid interface via mesoscopic computer simulations and compared to microgels with ideal (diamond-like) structure. The effect of crosslinkers reactivity ratio on the single particle morphology at the interface and monolayer behavior was examined. It was demonstrated that single particles deform into an explicit core-corona morphology when adsorbed at the interface. An increase in the crosslinker reactivity ratio decreased both the deformation ratio and the ratio between the core and corona sizes. Meanwhile, the compression of microgel monolayers revealed the existence of five distinct interparticle contact regimes, which have been observed experimentally in the literature. The crosslinker reactivity ratio appeared to define the compression range in these regimes and the sharpness of the transition between them. In particular, the higher the crosslinker reactivity ratio, the smaller the corona, and in turn, the narrower the range of the intermediate regime comprising both core-core and corona-corona contacts. The obtained results demonstrate that the more realistic model of microgels synthesized via precipitation polymerization allows for a more accurate prediction of the properties of the microgels at a liquid-liquid interface in comparison to the conventional diamond-like lattice model.

In the current work, atom transfer radical polymerization-induced self-assembly (ATRP PISA) phase diagrams were obtained by the means of dissipative particle dynamics simulations. A fast algorithm for determining the equilibrium morphology of block copolymer aggregates was developed. Our goal was to assess how the chemical nature of ATRP affects the self-assembly of diblock copolymers in the course of PISA. We discovered that the chain growth termination via recombination played a key role in determining the ATRP PISA phase diagrams. In particular, ATRP with turned off recombination yielded a PISA phase diagram very similar to that obtained for a simple ideal living polymerization process. However, an increase in the recombination probability led to a significant change of the phase diagram: the transition between cylindrical micelles and vesicles was strongly shifted, and a dependence of the aggregate morphology on the concentration was observed. We speculate that this effect occurred due to the simultaneous action of two factors: the triblock copolymer architecture of the terminated chains and the dispersity of the solvophobic blocks. We showed that these two factors affected the phase diagram weakly if they acted separately; however, their combination, which naturally occurs during ATRP, affected the ATRP PISA phase diagram strongly. We suggest that the recombination reaction is a key factor leading to the complexity of experimental PISA phase diagrams.

We studied the crystallization of semiflexible polymer chains in melts and poor-solvent solutions with different concentrations using dissipative particle dynamics (DPD) computer simulation techniques. We used the coarse-grained polymer model to reveal the general principles and microscopic scenario of crystallization in such systems at large time and length scales. It covers both primary and secondary nucleation as well as crystallites' merging. The parameters of the DPD model were chosen appropriately to reproduce the entanglements of polymer chains. We started from an initial homogeneous disordered solution of Gaussian chains and observed the initial stages of crystallization process caused in our model by orientational ordering of polymer chains and polymer-solvent phase separation. We found that the overall crystalline fraction at the end of the crystallization process decreases with the increasing polymer volume fraction while the steady-state crystallization speed at later stages does not depend on the polymer volume fraction. The average crystallite size has a maximal value in the systems with a polymer volume fraction from 0.7 to 0.95. In our model, these polymer concentrations represent an optimal value in the sense of balance between the amount of polymer material available to increase the crystallite size and chain entanglements, that prevent crystallites' growth and merging. On large time scales, our model allows us to observe lamellar thickening linear in logarithmic time scale.

Construction of chromosomes 3D models based on single cell Hi-C data constitute an important challenge. We present a reconstruction approach, DPDchrom, that incorporates basic knowledge whether the reconstructed conformation should be coil-like or globular and spring relaxation at contact sites. In contrast to previously published protocols, DPDchrom can naturally form globular conformation due to the presence of explicit solvent. Benchmarking of this and several other methods on artificial polymer models reveals similar reconstruction accuracy at high contact density and DPDchrom advantage at low contact density. To compare 3D structures insensitively to spatial orientation and scale, we propose the Modified Jaccard Index. We analyzed two sources of the contact dropout: contact radius change and random contact sampling. We found that the reconstruction accuracy exponentially depends on the number of contacts per genomic bin allowing to estimate the reconstruction accuracy in advance. We applied DPDchrom to model chromosome configurations based on single-cell Hi-C data of mouse oocytes and found that these configurations differ significantly from a random one, that is consistent with other studies.

We developed a theoretical model of linear ultrahigh molecular weight polyethylene (UHMWPE) homogeneous polymerization. We considered polymerization to be living and occurring in a poor solvent. We derived the dependency of the entanglement length on the chain length during this process. We assessed how the rate of polymerization and the concentration of initiators affect entanglement of chains. Theoretical predictions were supported by the molecular dynamics computer simulations of the coarse-grained model of polyethylene. The computer model implemented living polymerization of linear chains, poor solvent conditions, formation of entanglements, and crystallization of growing chains. Polyethylene chains were modeled by using specific angular potential with the three energy minima. Our theory and the simulation results pointed out that there are two stages of homogeneous polymerization. At first, the chains grow independently. When the chains become long enough, they start to entangle, and the entanglement length starts to decrease. We also observed in simulations the existence of the third stage, when the entanglement length grows with the chain length at the very high conversion degrees. Theoretical predictions and the simulation results showed that a decrease of the concentration of initiators leads to a decrease in the entanglement density in the resulting semicrystalline UHMWPE sample. Our theory also predicted the existence of an optimal reaction rate for obtaining semicrystalline UHMWPE samples with the highest possible entanglement length at a given concentration of initiators. Our work could be a guide how to obtain low-entangled UHMWPE samples by tailoring the reaction conditions.